Problem: Simplify the following expression: $k = \dfrac{-8p - 7}{p - 8} - \dfrac{-p - 19}{p - 8}$
Solution: Since the expressions have the same denominator we simply subtract the numerators: $k = \dfrac{-8p - 7 - (-p - 19)}{p - 8}$ Distribute the negative sign: $k = \dfrac{-8p - 7 + p + 19}{p - 8}$ Combine like terms: $k = \dfrac{-7p + 12}{p - 8}$